Guides

Every guide on this site follows the same shape: the standard it implements, the quantities that standard defines, the assumptions the implementation makes, then runnable code and the figure it draws. Nothing here is a survey of the field; each page is the working documentation of a module, written so that a result can be defended clause by clause rather than trusted.

This page is the map. A hundred and six guides sit in ten topics, and each topic has its own overview page with the longer story of how its pieces fit together. If you are arriving without a specific question, read Getting Started first: it runs one signal through the whole processing chain and gives the vocabulary the rest of the guides assume. If you already know the quantity you need, the glossary lists every symbol with its unit, its defining standard and the guide that implements it.

Two pointers before the list. Function signatures live in the API reference, which is generated from the docstrings and is not repeated here. Derivations, design decisions and the numerical evidence live in Reference: the theory pages explain why a formula is the one it is, and the conformance report shows the standard’s own expected value next to the computed one.

A third pointer, for anyone arriving with a measurement to make rather than a number to compute. Where a method needs a physical arrangement, its guide carries an engineering setup diagram with the geometry the standard prescribes: source and microphone positions, separations, mounting, and the specimen or the enclosing surface. Field Insulation Measurement draws the ISO 16283-1 room pair that way, and Impedance Tube draws the ISO 10534-2 tube with both microphone spacings. The prediction and rating guides take element or material data as their input instead and need no facility, which is usually the fastest way to tell the two kinds of page apart. What do you need to measure? sorts the same guides by the job rather than by the topic.

Filter banks, weighting, levels, spectra, calibration and uncertainty. This is the chain that turns a digital signal into a standards-compliant number, and every other area consumes it: a loudness model needs calibrated band levels, a room parameter needs a filtered impulse response, an environmental rating is an adjusted $L_{eq}$. Implements IEC 61260-1, ANSI S1.11, IEC 61672-1, ISO 7196, IEC 61252, ISO 1996-1, IEC 60942 and the GUM.

• Build a sound level meter: the whole area assembled end to end on one runnable page, from the calibrator tone to the reported levels.

Octave filtering

• Filter Banks: the fractional-octave band mathematics, the bank parameters, the parametric EQ, band decomposition and zero-phase offline filtering.
• Filter Architecture Gallery: the five filter architectures compared at the band edges, the full response gallery and per-architecture usage, with the Linkwitz-Riley crossover.
• Filter Class Verification (IEC 61260-1): the Table 1 acceptance mask band by band, the class 0 of the withdrawn 1995 edition and the compliance fiche.
• Block Processing: stateful streaming analysis that carries filter state across buffers, for signals that never fit in memory.
• Multichannel and Performance: vectorized analysis of many channels at once, with the (channels, samples) convention and performance notes.

Levels and weighting

• Frequency Weighting (A, C, Z): the IEC 61672-1 ear-response curves, the high-frequency accuracy mode and the Table 3 class verification.
• Special Weightings (G, B, D, AU): ISO 7196 G-weighting for infrasound, the historical B and D curves and AU for audible sound in the presence of ultrasound.
• Time Weighting: the Fast, Slow and Impulse exponential ballistics of IEC 61672-1.
• Integrated and Statistical Levels: $L_{eq}$ and $L_{Aeq}$, the percentile levels $L_{10}$/$L_{50}$/$L_{90}$, $L_{Cpeak}$ and SEL, and the noise dose.
• Environmental Levels (ISO 1996-1/-2): $L_{den}$, $L_{dn}$ and the composite rating levels, the tonal adjustment, the residual-noise correction and the uncertainty budget. It lives under Environment and transport, and is repeated here because it is the level definitions above aggregated over a day.
• Spanish Noise Regulation (RD 1367/2007): the corrected level $L_{Keq}$ with its $K_t$, $K_f$ and $K_i$ corrections, the evaluation periods and noise phases, the limit tables and the Article 25 compliance check. It lives under Environment and transport too.

Signals and spectra

• Calibrated spectral analysis: the Welch power and cross-spectral estimators with their random errors, chi-square confidence intervals and fractional-octave smoothing.
• Multiple and partial coherence: the ordinary, multiple and partial coherence of several correlated sources driving one response, and which source dominates each band.
• Time-frequency analysis: the calibrated STFT spectrogram in absolute dB SPL, and the zoom FFT that resolves tones closer than a practical FFT bin.
• Cepstrum, echoes and the envelope spectrum: quefrency analysis, echo detection with the reflection coefficient read off the cepstral peak, liftering and the envelope spectrum.
• Time synchronous averaging: extraction of a periodic waveform of known period, the comb filter that describes it and the choice of the number of averages.
• Machine fault frequencies: the kinematic fault-frequency families of rotating machinery (Norton & Karczub Section 8.4) drawn on top of a measured envelope spectrum: bearing BPFO, BPFI, BSF and cage frequencies, gear-mesh sidebands, induction-motor slip, pole-pass and rotor-slot harmonics, and blade-passing tones. It lives under Vibration and structure-borne sound, and is repeated here because it is the envelope spectrum above put to work.
• Correlation, time delay and envelope: correlation with its random errors, time-delay estimation by direct correlation and the GCC weightings, and the Hilbert envelope.
• Test signals and sample-rate tools: IEC 60268-1 tone bursts with exact gating, colored noise with an exact slope, resampling with a stated anti-alias specification and fractional delay.
• System measurement: complementary Golay pairs, sweeps shaped to an arbitrary target magnitude spectrum, and Kirkeby-regularized inversion of a measured response.

Calibration and uncertainty

• Calibration and dBFS: physical SPL calibration from a calibrator tone or a known sensitivity, and the digital full-scale mode.
• Compliance and verification: what a performance class asserts, the verifiers per stage, the conformance report, and the scope of the pattern-evaluation and periodic-test parts.
• Measurement uncertainty (GUM and Monte Carlo): the law of propagation of uncertainty and the Monte Carlo method, with expanded uncertainty and coverage intervals.
• Data qualification: the reverse arrangement and runs tests for stationarity, and the Rice level-crossing and peak statistics with the irregularity factor.

Loudness, sound quality, speech intelligibility, hearing and exposure. Where the core area asks how much sound there is, this one asks what a listener makes of it: how loud it seems, how sharp or rough or annoying, how much of a talker survives the room, and how much hearing a working life in that noise costs. Implements ISO 532-1/-2/-3, ECMA-418-1/-2, ISO 226, DIN 45692, IEC 60268-16, ANSI S3.5, DIN 45681, ISO/PAS 20065, ISO 7029, ISO 389-7, ISO 1999 and ISO 9612.

Psychoacoustics

• Loudness: loudness in sones by the ISO 532-1 Zwicker method with its one-page fiche, plus the ISO 226 equal-loudness contours.
• Advanced Loudness (ISO 532-2/-3, ECMA-418-2): the Moore-Glasberg stationary and time-varying methods and the Sottek Hearing Model loudness, with the model-choice table.
• Sound Quality Metrics: sharpness in acum, and the ECMA-418-2 tonality, roughness and fluctuation strength.
• Prominent Discrete Tones (ECMA-418-1): the tone-to-noise ratio and prominence ratio, with their frequency-dependent prominence criteria.
• Objective audibility of tones in noise (ISO/PAS 20065): the critical-band masking level, the masking index and the audibility of a tone above the masking threshold.
• Psychoacoustic annoyance and fluctuation strength: the Fastl and Zwicker annoyance model built from loudness, sharpness, roughness and fluctuation strength.

Speech

• Speech Transmission Index (STI): the modulation transfer function, the indirect method from an impulse response and the direct STIPA measurement.
• Speech Intelligibility Index: the SII in all four of the standard’s band procedures, with the band-importance functions, self-masking and upward spread of masking.
• Objective Intelligibility (STOI and ESTOI): the two correlation-based measures for time-frequency weighted noisy speech.

Hearing and exposure

• Hearing threshold (age and reference zero): the age-related threshold distribution of ISO 7029 and the ISO 389-7 reference threshold of hearing.
• Noise-induced hearing loss (ISO 1999): the permanent threshold shift as a function of level, duration and frequency, combined with the age component.
• Occupational Noise Exposure (ISO 9612): the task-based, job-based and full-day strategies for $L_{EX,8h}$, with the uncertainty budget and the upper limit.

Room parameters, background noise, field and laboratory insulation, and prediction from element data. Two questions run through the area: how a room treats the sound made inside it, and how much of the sound made next door gets through. Implements ISO 3382-1/-2/-3, ISO 16283-1/-2/-3, ISO 10140, ISO 10848, ISO 15186-1/-2, ISO 16251-1, ISO 717-1/-2, EN 12354-1 to -6, ISO 18233, ISO 12999-1, ISO 10052, ANSI/ASA S12.2 and ASTM E413/E1414.

Room acoustics

• Measuring the Room Impulse Response: the ISO 18233 deterministic acquisition, exponential sweeps with their deconvolution, and MLS.
• Room Acoustics: the room parameters EDT, $T_{20}$, $T_{30}$, $C_{50}$, $C_{80}$, $D_{50}$ and $T_s$ derived from that impulse response.
• Open-Plan Office Acoustics (ISO 3382-3): the spatial decay rate of speech and the distraction and privacy distances of an open-plan floor.
• Image sources and the steady-state room field: the deterministic image-source impulse response of a rectangular room, the room constant, critical distance and Schroeder frequency.
• Room-noise criteria (NC / RC Mark II): the ANSI/ASA S12.2 Noise Criteria rating by tangency, and the Room Criteria Mark II rating with its rumble, hiss or neutral tag.
• Reverberation-time prediction (Sabine, Eyring, Arau): five statistical-acoustics models from volume, boundary areas and surface absorption, including the air term.
• Sound absorption in enclosed spaces (EN 12354-6): the total equivalent absorption area of a room from its surfaces, objects and air, and the reverberation time that follows.

Sound insulation

• Field Insulation Measurement (ISO 16283): airborne and impact insulation measured in the building, its test report and the ISO 12999-1 uncertainty that qualifies it.
• Laboratory Insulation Measurement: the ISO 10140 characterisation of an element with flanking suppressed.
• Sound Insulation by Intensity (ISO 15186): the transmitted power read off the radiating face, for the whole element or element by element.
• Sound Insulation Survey Method (ISO 10052): the octave-band control method with its reverberation index and its airborne, impact, façade and service-equipment quantities.
• Laboratory Flanking Transmission (ISO 10848): the junction vibration reduction index and the flanking level differences measured on a test facility.
• Heavy and Soft Impact Sources (ISO 16283-2): the rubber ball and the bang machine: the impact force exposure level that specifies them, the laboratory check they have to pass, and the single number of ISO 717-2 Annex D.
• Insulation Ratings (ISO 717): the airborne and impact reference-curve engines with $C$, $C_{tr}$ and $C_I$, the enlarged-range terms and the ISO 717 fiche.
• Façade Sound Insulation: the building envelope measured per ISO 16283-3, predicted per EN 12354-3 and radiating outwards per EN 12354-4.
• Spanish Building Code (CTE DB-HR): the DB-HR global indices $R_A$, $R_{A,tr}$, $D_{nT,A}$ and $D_{2m,nT,Atr}$, the clause 2 requirement tables and the window-size correction.

Insulation design

• Predicting Sound Insulation (EN 12354): in-situ airborne and impact insulation between rooms from element data, with their flanking paths.
• Detailed Per-Band Prediction (ISO 12354): the same prediction band by band rather than as one number: in-situ element and junction data, the flanking index and impact level, and the per-path contributions behind R’w and L’n,w.
• Predicting Panel Sound Insulation: the mass law and coincidence dip, double walls, slits and apertures, plate radiation efficiency and point mobilities.
• Floor-Covering Impact Improvement (ISO 16251-1): the weighted improvement of a soft floor covering measured on a small heavyweight mock-up.
• Predicting Resilient-Layer Performance: the tapping-machine force model, the cut-off frequency of a soft covering, the floating-floor improvement laws and the ISO 12354-1 Annex D rating of a wall lining.
• Dynamic stiffness of resilient materials (EN 29052-1): the stiffness per unit area under a floating floor from the load-plate resonance, with the enclosed-gas term. It lives under Materials and surfaces, and is repeated here because it is the input the layer models above ask for.
• Structure-borne sound power of equipment (EN 15657): the reception-plate method and the plate-independent source quantities: equivalent blocked force, free velocity and source mobility. Also listed under Vibration, beside the mobilities it is built from.
• Installed structure-borne sound (EN 12354-5): the coupling term from source and receiver mobilities, the installed power and the per-path sound pressure level in the receiving room. Also listed under Vibration.

Absorption, airflow resistance, the impedance tube, porous and metamaterial models, diffusers and scattering. What a surface does to the sound that reaches it, measured in a laboratory or predicted from the material parameters. Implements ISO 354, ISO 11654, ISO 10534-1/-2, ISO 9053-1/-2, ISO 17497-1/-2, ISO 13472-1/-2, EN 29052-1 and ISO 12999-2.

Absorbers

• Sound Absorption Measurement and Rating: the ISO 354 reverberation-room measurement, the weighted rating and its class, and the measurement uncertainty of both.

• Airflow Resistance: the static and alternating determination of airflow resistance and resistivity.

• Impedance Tube: the normal-incidence surface impedance, absorption and transmission loss, plus the virtual FDTD tube.

• Porous and Multilayer Absorbers: the Delany-Bazley, Miki and Johnson-Champoux-Allard models, the transfer-matrix multilayer solver with perforated, microperforated and membrane layers, and the random-incidence integral.

• Metamaterial Absorbers: the critical-coupling condition for perfect absorption and the slow-sound slit panel loaded by Helmholtz resonators, with its design solver. Diffusers and surfaces

• Diffusers and Their Coefficients: the random-incidence scattering coefficient, the autocorrelation diffusion coefficient, and Schroeder design with its far-field prediction.

• Metadiffusers: deep-subwavelength Schroeder diffusers from resonator-loaded slits, slow sound and ternary sequences.

• In-situ Road-Surface Absorption: in-situ road-surface absorption by the subtraction technique and the spot method. It is the only guide of the surfaces measured in place overview, which the sidebar files in this same group.

Resilient layers

• Dynamic stiffness of resilient materials (EN 29052-1): the stiffness per unit area under a floating floor from the load-plate resonance, with the enclosed-gas term. Also listed under Rooms and buildings, beside the floating-floor prediction that consumes it.

Mobility and frequency-response functions, isolators, radiated power, junctions and human vibration. The area covers the path a machine takes into a structure and out again as airborne sound, and the separate question of what vibration does to the person exposed to it. Implements ISO 7626-1/-2, ISO 10846-1/-2/-3, ISO 9611, ISO/TS 7849-1/-2, EN 15657, EN 12354-5, ISO 2631-1/-2/-4/-5, ISO 5349-1/-2 and ISO 8041-1.

Structure-borne sources

• Mechanical mobility and the FRF family (ISO 7626-1): receptance, mobility and accelerance with their reciprocals, conversion between them, and the closed-form single-degree-of-freedom resonator.
• Bending-wave transmission at plate junctions: the wave-approach transmission coefficients for rigid X, T, L and in-line junctions, their diffuse-field average, and the coupling loss factor and vibration reduction index.
• Transfer stiffness of resilient elements (ISO 10846): the dynamic transfer stiffness and loss factor of an isolator by the direct and indirect methods.
• Sound power from surface vibration (ISO/TS 7849): the radiated power from the surface-averaged velocity level and the radiation factor, with the Part 1 upper limit and the Part 2 engineering value. It lives under Sources and devices, and is repeated here because its input is a measured surface velocity.
• Structure-borne sound power of equipment (EN 15657): the reception-plate method and the plate-independent source quantities, equivalent blocked force, free velocity and source mobility. It lives under Rooms and buildings, and is repeated here because the source quantities are mobilities.
• Installed structure-borne sound (EN 12354-5): the coupling term from source and receiver mobilities, the installed power and the per-path sound pressure level in the receiving room. It lives under Rooms and buildings, for the same reason.

Human vibration

• Human Vibration: whole-body and hand-arm exposure with the ISO 8041-1 weightings, the weighted r.m.s. and dose measures, and the daily exposure $A(8)$.
• Multiple-shock whole-body vibration (ISO 2631-5): the seat-to-spine transfer function, the acceleration dose, and the cumulative stress variable behind the lumbar injury probability.

Machinery

• Machine fault frequencies: the characteristic bearing, gear and shaft frequencies and the envelope analysis that finds them under the broadband noise of a running machine. Also listed under Signal analysis, beside the spectral estimators it uses.

Outdoor propagation, barriers, refraction, road, rail and wind-turbine sources, and the assessment built on them. Everything here concerns sound that has to travel a long way before it is assessed, so the atmosphere, the ground and the source’s own motion all enter the answer. Implements ISO 9613-1/-2, ISO 1996-1/-2, ISO/PAS 1996-3, NT ACOU 112, CNOSSOS-EU (2002/49/EC Annex II) and IEC 61400-11.

One scope boundary is worth stating here rather than one click away. Of CNOSSOS-EU, what is implemented is the source side of Annex II: the road emission of section 2.2 with the Appendix F coefficients, and the railway emission of section 2.3 with Appendix G, which give the directional sound power per metre of source line. The propagation calculation of section 2.5, with its own ground, diffraction and favourable-conditions machinery, is not implemented; outdoor attenuation here goes through the ISO 9613-2 chain instead, which is a different model and not interchangeable with it for regulatory mapping.

Outdoor sound

• Outdoor Sound Propagation: atmospheric absorption and the ISO 9613-2 general method, with a per-term octave-band attenuation breakdown.
• Spherical ground effect and advanced barriers: the Weyl-Van der Pol reflection coefficient over finite-impedance ground, and wave-theoretic barrier diffraction.
• Atmospheric refraction: rays and the GFPE: effective sound-speed profiles, curved rays with a closed-form shadow-zone distance, and the GFPE relative-level field.

Sources

• CNOSSOS-EU road traffic source emission: the common EU road source of Annex II 2.2: rolling and propulsion sound power per vehicle category and the directional power per metre of source line.
• CNOSSOS-EU railway source emission: the rail source of Annex II 2.3: roughness and the contact filter, impact noise, curve squeal, traction and aerodynamic noise, and the two equivalent source lines.
• Wind-turbine noise: sound power and tonal audibility: the apparent sound power level referred to the rotor centre, and the tonal audibility chain that decides whether a tone is audible.

Assessment and regulation

• Impulsive-sound prominence (NT ACOU 112): the predicted prominence of each impulse from its onset rate and level difference, and the adjustment added to $L_{Aeq}$.

• Environmental Levels (ISO 1996-1/-2): $L_{den}$, $L_{dn}$ and the composite rating levels, the tonal adjustment, the residual-noise correction and the uncertainty budget. Also listed under Signal analysis, beside the level definitions it builds on.

• Spanish Noise Regulation (RD 1367/2007): the corrected level $L_{Keq}$ with its $K_t$, $K_f$ and $K_i$ corrections, the evaluation periods and noise phases, the limit tables and the Article 25 compliance check. Also listed under Signal analysis, for the same reason.

Certification levels, airport contours and the rotorcraft hemisphere method: the noise of flight measured the way the certification and airport-planning documents prescribe. Implements ICAO Annex 16, IEC 61265, SAE ARP 866B/5534 and ECAC Doc 29/32.

• Aircraft noise: Effective Perceived Noise Level: perceived noisiness and PNL, the tone correction, the duration correction and the measurement-system verifier.
• Airport Noise (ECAC Doc 29): the noise-power-distance engine, the per-segment single-event chain and the ground-grid SEL contour.
• Rotorcraft noise: the hemisphere method: the hemisphere source model with its propagation adjustments, flight-condition interpolation, and the single-event contours.
• The ANP fleet database: the EASA tables of noise-power-distance curves and default trajectories, and the Doc 29 chain run from an aircraft identifier.

Levels referenced to 1 micropascal, ship radiated noise, pile driving, ambient noise and propagation loss. The reference quantities differ from the airborne ones, so this is the one area where a level cannot be read across without conversion. Implements ISO 18405, ISO 17208-1/-2, ISO 18406 and JOMOPANS-ECHO.

• Underwater acoustics: radiated noise and pile driving: the ISO 18405 reference levels, the ship radiated noise level and equivalent monopole source level, and single-strike and cumulative pile-driving exposure.
• Underwater sound propagation: spreading plus volume absorption, the speed of sound in sea water, the sonar equation, seabed reflection loss and the ambient-noise spectrum.
• Underwater propagation solvers: the normal-mode, ray-tracing and parabolic-equation solvers of the stratified waveguide, and how to choose a propagation model.
• Marine-mammal noise exposure: the hearing side of that noise: the group audiograms, the regulatory weighting functions with their guidance version, and the exposure of a pile-driving campaign against the injury criteria.

Sound power, intensity, emission declarations, electroacoustics and programme loudness. What a source emits rather than what a receiver gets, plus the electroacoustic chain that reproduces or measures it. Implements ISO 3741, ISO 3744/3746, ISO 3745, ISO 9614-1/-2/-3, IEC 61043, ISO 4871, IEC 60268-3/-4/-5, ITU-R BS.1770-5 and EBU R 128.

Sound power and intensity

• Sound Intensity (p-p): two-microphone intensity with the field indicators that qualify the measurement.
• Sound Power: choosing the determination method and declaring the noise emission per ISO 4871.
• Sound Power by Pressure Methods: the enveloping surface of ISO 3744/3746 and the precision anechoic grade of ISO 3745.
• Sound Power in the Reverberation Room: the direct and comparison methods of ISO 3741.
• Sound Power by Intensity Scanning: the on-site scanning of ISO 9614-2 and the ISO 9614-3 precision grade.
• Sound power from surface vibration (ISO/TS 7849): the fourth determination route, for the machine that cannot be moved into a qualified room: the radiated power from the surface-averaged velocity level and the radiation factor, with the Part 1 upper limit and the Part 2 engineering value. Also listed under Vibration.

Electroacoustics

• Electroacoustics: distortion and frequency response: harmonic and intermodulation distortion, THD+N and SINAD, dynamic range and the $H_1$/$H_2$ frequency-response estimators.

• Loudspeaker Characterisation (IEC 60268-5): the sensitivity conventions, the radiating piston and the characteristics fiche.

• Microphone Characterisation (IEC 60268-4): the sensitivity references, the directional patterns and the inherent noise.

• Swept-sine distortion and phase utilities: harmonic separation from one exponential sweep, THD against excitation frequency, and minimum phase, group delay and excess phase. Broadcast

• Programme loudness and true peak: K-weighting and gated integrated loudness in LUFS, the momentary and short-term meters, the loudness range and the true-peak level. The sidebar files it inside Electroacoustics; it has its own section overview.

Noise control

• Silencers: reactive silencers by the four-pole transmission-matrix method and the reactive-versus-dissipative choice.
• Duct-Borne Noise: Fan to Room: the end-to-end fan-to-room calculation against a room criterion, and the higher-order-mode cut-on that limits every plane-wave method.
• Room to Room: Partition, Receiving Room, Criterion: the source-room level through a partition into the receiving room, the noise criterion verdict and the transmission loss a partition or an enclosure needs.
• Industrial Noise Control: HVAC and Enclosures: duct attenuation and flow noise, and enclosure insertion loss.

Deterministic 2D finite-difference time-domain solvers, acoustic and elastic P-SV, validated against analytic oracles rather than a standard. It is the one area with no governing document, so its evidence is the closed-form solution it reproduces.

• 2D FDTD wave simulation: a staggered pressure-velocity grid with Gaussian, tone and arbitrary-signal sources, rasterised obstacles, rigid, impedance and absorbing boundaries, and a frozen result carrying probe histories and field snapshots.
• Elastic waves and fluid-solid coupling: the P-SV companion solver on the same grid, with Rayleigh waves on free surfaces, mode conversion, Scholte interface waves and immersed-plate transmission.